On the new universality class in structurally disordered $n$-vector model with long-range interactions

TL;DR

This paper investigates the stability boundary of a new universality class in long-range interacting $n$-vector models with structural disorder, using renormalization group techniques to determine the critical parameters and their implications.

Contribution

It introduces a three-loop $oldsymbol{ ext{epsilon}}$-expansion for the marginal dimension $n_c$, providing numerical estimates and showing the universality class applies beyond Ising systems.

Findings

Identifies the stability border for the new universality class.

Provides numerical estimates for the marginal dimension $n_c$.

Shows the universality class includes systems with $n=1$ in 2D and 3D.

Abstract

We study a stability border of a region where nontrivial critical behaviour of an $n$-vector model with long-range power-law decaying interactions is induced by the presence of a structural disorder (e.g. weak quenched dilution). This border is given by the marginal dimension of the order parameter $n_c$ dependent on space dimension, $d$, and a control parameter of the interaction decay, $\sigma$, below which the model belongs to the new dilution-induced universality class. Exploiting the Harris criterion and recent field-theoretical renormalization group results for the pure model with long-range interactions we get $n_c$ as a three loop $\epsilon=2\sigma-d$-expansion. We provide numerical values for $n_c$ applying series resummation methods. Our results show that not only the Ising systems ($n=1$) can belong to the new disorder-induced long-range universality class at $d=2$ and $d=3$.